Question

which of the following are solutions to the quadratic equation? check all that apply. 2x^2+9x-3=-x^2+xa. -2b. 1/3c. 1d. 3e. -1/2f. -3

Answer 1

We have to check which one of the numbers given are solutions of the equation:

`\begin{gathered} 2x^2+9x-3=-x^2+x \\ 2x^2+x^2+9x-x-3=0 \\ 3x^2+8x-3=0 \end{gathered}`

For doing so, we will replace each one of the values onto the equation, and if both sides of the equation remains the same, we will get a solution.

a: x=-2

In this case,

`\begin{gathered} 3(-2)^2+8(-2)-3=3(4)+16-3 \\ =12-16-3 \\ =-4-3 \\ =-7 \end{gathered}`

And as it's not equal to zero, its not a solution.

b: x=1/3

In this case

`\begin{gathered} 3((1)/(3))^2+8((1)/(3))-3=(3)/(9)+(8)/(3)-3 \\ =(1)/(3)+(8)/(3)-3 \\ =(9)/(3)-3 \\ =3-3=0 \end{gathered}`

And as it's equal to zero, it's a solution.

c: x=1

In this case

`\begin{gathered} 3(1)^2+8(3)-3=3+24-3 \\ =27-3 \\ =24 \end{gathered}`

So, 1 is not a solution

d: x=3

In this case,

`\begin{gathered} 3(3)^2+8(3)-3=3(9)+24-3 \\ =27+24-3 \\ =48 \end{gathered}`

So 3 is not a solution.

e: x=-1/2

In this case,

`\begin{gathered} 3(-(1)/(2))^2+8(-(1)/(2))-3=3((1)/(4))-(8)/(2)-3 \\ =(3)/(4)-4-3 \\ =(3)/(4)-7 \\ =(3)/(4)-(28)/(7) \\ =-(25)/(7) \end{gathered}`

So -1/2 is not a solution.

f: x=-3

In this case,

`\begin{gathered} 3(-3)^2+8(-3)-3=3(9)-24-3 \\ =27-24-3 \\ =3-3 \\ =0 \end{gathered}`

This means that 3 is a solution of the equation.